Interpolation for Brill–Noether curves Page 1 Forum of Mathematics, Pi (2023), Vol. 11:e25 1–90
doi:10.1017/fmp.2023.22 RESEARCH ARTICLE Interpolation for Brill–Noether curves Eric …

A fundamental problem in the theory of algebraic curves in projective space is to understand
which reducible curves arise as limits of smooth curves of general moduli. Special cases of …

A classical fact is that through any $ d+ 3$ general points in $\mathbb {P} _\mathbb {C}^ d $
there exists a unique rational normal curve of degree $ d $ passing through them. We …

Abstract Let X= X 1∪⋯∪ X s⊂ P n, n≥ 4, be a general union of smooth non-special curves
with X i of degree di and genus gi and di≥ max {2 gi-1, gi+ n} if gi> 0. We prove that X has …

For all integers $ n, d, g $ such that $ n\ge 4$, $ d\ge n+ 1$, and $(n+ 2)(dn-1)\ge n (g-1) $,
we define a good (ie generically smooth of dimension $(n+ 1) d+(3-n)(g-1) $ and with the …

Let $ X= X_1\cup\cdots\cup X_s\subset\mathbb {P}^ n $, $ n\ge 4$, be a general union of
smooth non-special curves with $ X_i $ of degree $ d_i $ and genus $ g_i $ and …

We study the Hilbert function of general unions of non-special embeddings of general
curves in projective spaces, mostly in P4, the case of a general non-special curve of …

We prove the existence of a smooth and non-degenerate curve X⊂ Pn, n, with deg (X)= d,
pa (X)= g, h (NX (−))=, and general moduli for all (d, g, n) such that d (n−) g+ n+. It was …

Fix a hyperplane H;⊂..., n > 3, and a finite set S;⊂ H. We give conditions on the integers
d, g and#(S) such that there exists a smooth and connected curve X;⊂... with deg (X)= d, p< …